Area of Triangles Under a Curve

Given: Right triangle BCD whose hypotenuse is tangent to the function f(x) = a/x. 

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1. Move slider a and observe what happens? How is the appearance of the graph relate to a?
2. Move point A and observe the triangle? What do you observe?
3. What conjecture can you make based on your observation in 2. Prove your conjecture. 

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